The Cyberium was an AI which contained the knowledge and future history of all Cybermen, (TV: The Haunting of Villa Diodati) serving a role once held by the history computer. (TV: The Tomb of the Cybermen, PROSE: Iceberg, et al.)
Initially used by the Cybermen (TV: The Haunting of Villa Diodati) during the Cyber-Wars of an era that the Thirteenth Doctor described as the "very far future", (TV: Ascension of the Cybermen) the Cyberium was eventually acquired by a resistance force known as the Alliance, who sent it back in time (TV: Fugitive of the Judoon) to Earth in 1816. From here, the Cyberium frequently switched hosts: Percy Shelley was its initial "guardian", before being briefly possessed by the Thirteenth Doctor, who was forced to relinquish the Cyberium to Ashad, the Lone Cyberman. Ashad then time travelled (TV: The Haunting of Villa Diodati) to the immediate aftermath of the Cyber-Wars and attempted to restore the Cyber-Empire, (TV: Ascension of the Cybermen) until the Spy Master murdered him and used the Cyberium to create the CyberMasters. (TV: The Timeless Children)
The Cyber-Wars and the Alliance
During the Cyber-Wars of an era that the Thirteenth Doctor described as "the very far future", (TV: Ascension of the Cybermen) the Cybermen used the Cyberium; the Doctor would describe the Cyber-Wars as "an epic battle", with the Cyberium "at the heart of it, controlling data, strategy [and] decision making". (TV: The Haunting of Villa Diodati)
Sometime either late in the Cyber-Wars or during the immediate aftermath of the conflicts, (TV: Ascension of the Cybermen) a resistance group known as the Alliance captured the Cyberium and sent it back through time and space in order to prevent the Lone Cyberman from resurrecting the Cyber-Empire. In the 21st century, Captain Jack Harkness informed the Thirteenth Doctor's companions, Graham O'Brien, Yasmin Khan and Ryan Sinclair, about this, but did not specify exactly what the Alliance had sent back, though he did tell the trio to send the Doctor a warning, telling her to "beware [of] the Lone Cyberman" and not to "give it what it [wanted]". (TV: Fugitive of the Judoon)
Percy Shelley, the "guardian"
The Cyberium arrived on Earth in 1816. Percy Shelley found the Cyberium in Lake Geneva; when he recovered it, the Cyberium melted into his hand and entered his bloodstream. Upon returning to Villa Diodati, the Cyberium tried to hide itself by making Shelley invisible to everyone else and even utilised a perception filter on the Villa to keep itself from being discovered. Meanwhile, Shelley acted as its guardian, although the sheer amount of data processing through Shelley's mind, ranging from vast quantities of code to the battles of the Cyber-Wars, began to drive him mad, and so he hid in the Villa's cellar.
Meanwhile, the Thirteenth Doctor, Ryan, Yaz and Graham were visiting Mary Godwin, Lord Byron, Claire Clairmont and Dr John Polidori in Villa Diodati, when the Lone Cyberman - whose original name was Ashad - invaded the Villa in search of the Cyberium. Though a long-standing enemy of the Cybermen, this was the Doctor's first encounter with the Cyberium, initially displaying an unfamiliarity with the term.
When the Doctor was finally able to locate Shelley, she had him tell her what happened, noticing that the Cyberium was burning through Shelley's mind and would destroy him if it stayed in him much longer. Despite his efforts to stop Ashad from teleporting into the cellar, Shelley relented, as per the Doctor's advice, and Ashad confronted Shelley, demanding that the group surrender the Cyberium or he would kill Mary, Shelley's partner. However, in order to be extracted, the Cyberium had to leave Shelley willingly.
The Doctor proceeded to use an "old Time Lord trick" to manipulate Shelley's mind to show the poet his future death, which tricked the Cyberium into leaving his body, believing Shelley to be dead. After disabling the perception filter on the Villa, the Cyberium entered the Doctor's body; the Doctor claimed that her "Time Lord magnetism" implied that she was the Cyberium's true guardian. However, when Ashad threatened to destroy the Earth with his cyber-ship, the Doctor released the Cyberium to Ashad, who instantly teleported to his ship and travelled back to the future, (TV: The Haunting of Villa Diodati) in the immediate aftermath of the Cyber-Wars.
Ashad, resurrector of the Cyber-Empire
As the Doctor reasoned, she was recognised by the Cyberium's memory as an enemy of the Cybermen. Believing the Cyberium to see all, Ashad felt that it had given him understanding and distilled his purpose, leading him to regard himself as the perfect vessel for the ascension of the Cybermen and the death of their enemies.
With the knowledge of the Cyberium, Ashad and his Cyberguards travelled to a refugee planet and attempted to kill what few humans were left on the planet, including the Doctor, Ryan, Yaz and Graham, who had followed Ashad. When Graham and Yaz escaped with refugees Ravio, Yedlarmi and Bescot in one of the Cybermen's Cyberfighters, Ashad and his Cyberguards followed in a spare Cyberfighter. The trio of Cybermen followed the humans to the ruins of one of the final battles of the Cyber-Wars, in particular to an abandoned Cybercarrier - which the Cyberium had informed Ashad of - and Ashad began reviving the ship's army of Cyber-Warriors, who attempted to kill the humans onboard the Cybercarrier. (TV: Ascension of the Cybermen)
The Master's alliance with the Cyberium
After the Spy Master invited Ashad and the Cybermen to Gallifrey via the Boundary, Ashad and the Master met in the Capitol, where the Master was interested to learn that Ashad was the host of the Cyberium. Ashad revealed that the Cyberium had created, through him, the death particle, in order to eradicate all organic life after the Cybermen had erased all organic components from their systems. The Master, disappointed by Ashad's plan, offered to ally with him to ensure that the Cybermen became the true dominant species of the universe.
Onboard the Cybercarrier, the Master and Ashad entered a mass cyber-conversion chamber, and the Time Lord attempted to coax the Cyberium from Ashad; when the Lone Cyberman stated that the Cyberium would not leave him while he remained alive, the Master killed Ashad with his Tissue Compression Eliminator, releasing the Cyberium. The Master proposed that he become the Cyberium's new host, noting that the latter knew all the knowledge of the Cybermen, while he knew all the knowledge of the Time Lords after ransacking the Matrix. The Cyberium agreed and took the Master as its new host. Together, the Master and the Cyberium created the CyberMasters, Cybermen with Time Lord regenerative abilities, converted from the Time Lords murdered by the Master when he ravaged Gallifrey after learning of the nature of the Timeless Child.
Eventually, the Master, with the Cyberium fused into his mind, unveiled the CyberMasters to the Doctor in the heart of the Capitol. After leaving the Doctor trapped in a paralysis field, the Master returned with the CyberMasters to the heart of the Capitol, and teased the Doctor over her inability to kill him, the Cyberium and the CyberMasters when she needed to. At that moment, Ko Sharmus entered and persuaded the Doctor to escape and allow him to kill the Master in her place, explaining that he was originally part of the Alliance who sent the Cyberium back through time and space, and felt guilty for the events that had happened as a result. Immediately after the CyberMasters shot him, Ko Sharmus triggered a bomb which detonated the miniaturised death particle within Ashad's shrunken corpse, as the Master ordered the CyberMasters to escape with him and the Cyberium. (TV: The Timeless Children)
When Jack Harkness reunited with the Thirteenth Doctor, he was horrified to discover that the Cybermen had reclaimed the Cyberium but the Doctor assured him that she had handled it. (TV: Revolution of the Daleks)
The more common form assumed by the Cyberium was a floating mass of silver liquid metal that distorted in shape. (TV: The Haunting of Villa Diodati, The Timeless Children) However, when initially discovered by Percy Shelley on Earth in 1816, the Cyberium resembled a small, shiny, silver pebble-like object, which Shelley described as resembling quicksilver. Upon being retrieved by Shelley, the Cyberium "melted" into the poet's body, and appeared to flow through Shelley's veins like an electric-blue and white liquid. (TV: The Haunting of Villa Diodati)